two competing effects ofvolatiles on heat transfer in ...ruprecht/site/... · two competing effects...

Two Competing Effects of Volatiles on HeatTransfer in Crystal-rich Magmas: ThermalInsulation vs Defrosting

CHRISTIAN HUBER1!, OLIVIER BACHMANN2 ANDMICHAEL MANGA1

1DEPARTMENT OF EARTH AND PLANETARY SCIENCE, UNIVERSITY OF CALIFORNIA, BERKELEY, CA 947720-4767, USA2DEPARTMENT OF EARTH AND SPACE SCIENCES, UNIVERSITY OF WASHINGTON, SEATTLE, WA 98195-1310, USA

RECEIVED MAY 4, 2009; ACCEPTED JANUARY 8, 2010ADVANCE ACCESS PUBLICATION FEBRUARY 9, 2010

The build-up and eruption of crystal-rich ignimbrites, commonlyreferred to as ‘Monotonous Intermediates’, has been attributed to theincremental addition of new magma batches and the episodic partialmelting and reactivation of rheologically locked crystal-rich magmabodies (mushes). In this study, we explore the role of volatilesexsolved from a hot intrusion underplating a crystal mush on the ther-mal evolution of the coupled mush^intrusion system. We solve theenthalpy conservation equation for the mush and the intrusion andinvestigate the exsolution of volatiles from the intrusion and theirtransport through the mush in one dimension. Our calculations spana range of pressures (from 1 to 4 kbar), mush composition (andesiteto rhyolite) and initial water contents (from 1·5 to 6 wt %).Themobility of volatiles in the mush is controlled by the volume fractionof the pore space they occupy, and, as a consequence, by the amountof melting and the injection rate of volatiles from the intrusion tothe mush.We find that volatiles affect the melting of the mush (ordefrosting) in two opposite ways depending on pressure and the ini-tial water content of the intrusion.When the intrusion volatile con-tent is high and pressure relatively low (44 wt % H2O at 2 kbar),the mass transfer of volatiles from the intrusion to the mush carriesenthalpy beyond the melting front and can thus enhance defrostingand possibly remobilization of the mush. For lower initial volatilecontents (54 wt % H2O) in the intrusion and/or higher pressure(3^4 kbar), volatiles stall at the interface between the two magmabodies and prevent defrosting as they thermally insulate the mushfrom the intrusion.We propose that the dual role played by volatilesduring the thermal evolution of crystal-rich magmas reheated by anunderplating intrusion can explain the presence of crystal-rich

ignimbrites in arcs and their absence in drier hotspots or extensionalregions.

KEY WORDS: magma chamber; mush; intrusion; volatiles; defrosting;thermal insulation

I NTRODUCTIONMagma bodies spend the majority of their supra-solidusexistence in the crust as high-crystallinity mushes; in sucha high-crystallinity state, the lower degree of thermal dis-equilibrium with their surroundings, the inability to con-vect and latent heat buffering efficiently reduce theircooling rate (Marsh, 1981; Koyaguchi & Kaneko, 1999,2000; Huber et al., 2009). It is therefore expected that newmagmatic inputs rising from the mantle and deep crustwill often interact with crystal mushes. This interactionbetween a mature, high-crystallinity magma body andfresh intrusions plays a central role in the constructionand protracted existence of large magmatic systems(Mahood, 1990; Reid et al., 1997; Lipman, 2007).As magma bodies grow in the crust, they perturb the

local stress field and act as a focusing lens for new injec-tions of magma (Karlstrom et al., 2009). When twomagmas enter into contact, the dynamics and the amountof mixing between them depends on their respective vis-cosity, density and the injection rate (Huppert & Sparks,

!Corresponding author. E-mail: [email protected] [email protected]

! The Author 2010. Published by Oxford University Press. Allrights reserved. For Permissions, please e-mail: [email protected]

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1980; Jellinek et al., 1999; Snyder, 2000). In the ubiquitouscase where the mush is more evolved than the intrusion,the more mafic and dense magma input spreads under-neath the mush and acts as a heating plate with littlechemical mixing as a result of density stratification andrheological contrast (Couch et al., 2001). As the lowermagma cools and partially crystallizes, it exsolves andreleases buoyant volatiles that will migrate upwards to thecontact between the two magma bodies. The rate of vola-tile injection into the mush is controlled by the coolingrate and convective motion of the underplating magma(Eichelberger, 1980; Huppert et al., 1982; Cardoso &Woods, 1999). The collection of volatiles at the magmainterface (rheological barrier) leads to the formation of abuoyant instability that can eventually overcome the rheo-logical barrier and enter the mush once the volume frac-tion of gas and therefore the buoyancy of the foamy layerreaches a critical value (Eichelberger, 1980).Bachmann & Bergantz (2006) hypothesized that the vol-

atiles exsolved from an underplating magma wouldenhance the remobilization of crystal mushes because oftheir ability to increase the vertical heat transfer. Theirnumerical model does not solve for the enthalpy couplingbetween the two magmas (the intrusion was treated as afixed temperature boundary condition) and therefore doesnot solve for the injection rate of volatiles from the intru-sion to the mush. The crystal mush was also not allowedto melt during the course of their calculations.Building on this earlier model of gas sparging, this study

addresses the following questions:

(1) What features control the mobility of volatilesthrough a mush?

(2) Can the vertical transport of volatiles enhance or pre-vent the defrosting (partial melting of the crystallineframework) of a mush (see Mahood, 1990)?

(3) What is the effect of the mush composition on thethermal evolution of both magma bodies?

(4) What explains the paucity of crystal-rich ignimbritesin ‘dry’ (extensional, hotspot) tectonic environments?

To address these questions, we have developed aone-dimensional numerical model that solves for the com-bined thermal evolution of the two magma bodies. Wealso solve for the exsolution rate and transport of volatilesfrom the intrusion into the mush. Enthalpy conservationin the mush allows us to calculate the evolution of theporosity during partial melting of the mush locally andaccounts for changes in permeability by using a parameter-ization of the temperature^crystallinity relationship. Thecalculations span a range of pressures (from 1 to 4 kbar atthe level of the intrusion), a range of compositions for themush (through temperature^crystallinity parameteriza-tion) and a range of initial water contents for the intrusion(from 1·5 to 6wt % water).

PHYSICAL MODELWe solve for the heat and volatile mass transfer between ahot intrusion and a crystal mush (seeTable 1 for mathemat-ical symbols and Fig. 1 for a schematic illustration of thephysical model). For simplicity, the intrusion is emplacedinstantaneously and the volume ratio between the mushand the intrusion is kept constant at a ratio of 4:1. Thecolder crystalline mush is initially set at a uniform crystal-linity (55 vol. %) and temperature (which depends on thecrystallinity^temperature relation used). As the underplat-ing magma cools at the contact with the mush (coolingfrom below the intrusion is neglected here, for simplicity),it partially crystallizes, can reach volatile saturation andstarts exsolving a volatile phase. The volatile phase consistsmostly of water, as we assume that a large fraction of anyCO2 in the magma has already degassed before reachingthe depth of the intrusion ("4 kbar). The whole-rock com-position of the intrusion is assumed to be andesitic and weuse a different crystallinity^temperature relationship forthe mush to understand the importance of its compositionon the thermal evolution of both magmas. The mush isassumed to be initially saturated with volatiles and weneglect any volatile dissolution or exsolution that isexpected to arise as a consequence of both reheating andpartial melting of the mush. Furthermore, we assume thatvolatile transfer from the andesitic intrusion to the mushcarries heat but does not change the stability of the differ-ent minerals (i.e. we do not track the activity of water inthe volatile phase). Neglecting changes in the stabilityfield of different mineral phases in the mush upon the injec-tion of volatiles is a reasonable assumption as the kineticsassociated with the growth or dissolution of mineralscaused by changing the exsolved gas composition in themush are much slower than melting by heat transfer.

THE UNDERPLAT ING MAGMAWe assume that the crystal mush provides the main resis-tance to heat flow in the underplating magma^crystalmush system. We consider only heat transfer between theintrusion and the mush and do not account for coolingthrough the surrounding wall-rocks. Therefore, all the cal-culations that follow provide underestimates of the coolingrate, and as a consequence, the exsolution rate for theintrusion. We simplify the heat balance for the underplat-ing magma:

dTdt

# $ qoutciriHi|!!{z!!}

sensible heat

% Li

ci@wi@t|!!{z!!}

latent heat

&1'

where the first term on the right-hand side is sensible heatand the second term is latent heat; the subscript i refers tothe intrusion, Hi, Li, ci, ri and wi are respectively the thick-ness, the latent heat of crystallization, the specific heat,

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the density and the crystallinity of the underplatingmagma body and qout is the heat transfer from theintrusion to the mush. This heat balance equation assumesa well-mixed intruding magma with negligible thermalgradients; this is a relatively good approximation for a con-vecting magma body with strong temperature-dependentviscosity. The dynamic viscosity of the magma in theintrusion depends both on temperature and crystallinity(Dingwell et al., 1993):

m&T'

# m0 expQ

RTini

Tini

T$ 1

" #$ %1% 0 ( 75 w&T'=wcr

1$ w&T'=wcr

$ %2

&2'

where Q is the activation energy (fixed here at 500 kJ/mol),R is the ideal gas constant,Tini is the reference temperature(equal to the temperature during emplacement) andwcr# 0·5 is the critical crystallinity at which the intrusion

behaves like a solid.To calculate qout we need an expressionfor the thermal gradient at the interface between the twomagmas and thus the boundary layer thickness. The con-vection of a fluid with strongly temperature-dependentviscosity is parameterized in terms of the Rayleighnumber:

Ra # rag!TeH3

mk&3'

where r is the average density of the convecting fluid, a isthe thermal expansion coefficient, k is its thermal diffusiv-ity, H is the thickness of the fluid layer, and g is theacceleration due to gravity. This definition of Ra impliesthat the boundary conditions for the intrusion are pre-scribed temperatures, which is a good approximation aslong as the time step in the calculations is much shorterthan the cooling timescale. In all the following calcula-tions, Ra never decreases below 105 in the intrusion.

Table 1: List of parameters and symbols

Symbol Description Value Units

A Constant relating permeability to porosity 2) 10$12 m2

b Exponent relating temperature to crystallinity for mush 0·4, 0·5, 0·7, 1

cx Specific heat for phase J/kgK

dg Distance of penetration of volatiles in mush m

dm0 Distance of melting front (no volatiles) m

dm1 Distance of melting front (with volatiles) m

g Acceleration due to gravity m/s2

H Mush thickness 2000 m

kcond Thermal conductivity at intrusion–mush interface 2 W/mK

kg, ks, km Thermal conductivity of volatile, crystals and melt 0·31, 1·4, 2 W/mK

k and kr Permeability and relative permeability (mush or intrusion) m2

Li and L Latent heat of crystallization (intrusion and mush) 270 kJ/kg

Q Activation energy for dynamic viscosity 500 kJ

R Ideal gas constant 8·314 J/Kmol

S Surface area of contact between intrusion and mush 2) 108 m2

Sg Pore volume fraction occupied by volatiles

Tini Initial temperature of intrusion 850 8C

!Te Temperature difference driving convection in the intrusion 8C

ud,z Vertical component of Darcy velocity for volatile phase (mush) m/s

Vi Volume of intrusion 1011 m3

a Expansion coefficient (thermal and crystallinity) 3) 10–5 1/T

d Boundary layer thickness between mush and intrusion m

wi and wmush Crystallinity of intrusion and mush

wcr Critical crystallinity 0·5

k Thermal diffusivity 10$6 m2/s

rx Density of a given phase kg/m3

mx Dynamic viscosity of a given phase Pa s

HUBER et al. VOLATILES’ EFFECTS ON MAGMA

849




The assumption of a well-mixed intrusion magma is there-fore valid. The temperature difference responsible for con-vection (!Te has given by Davaille & Jaupart (1993)):

!Te # $2 ( 24 m&T'dm=dT

: &4'

The boundary layer thickness d between the twomagmas depends on the Rayleigh number of the andesiticmagma body:

d # d0Ra0Ra&t'

$ %1=3&5'

where d0 and Ra0 are the initial boundary layer thicknessand Rayleigh number. The heat exchange between thetwo magmas becomes

qout # $kcond@T@z

&&&&z#interface

$L@wmush

@t

&&&&z#interface

&6'

where kcond is the thermal conductivity at the interface andwmush is the crystallinity of the mush. qout is the thermalcoupling between the two magmas and requires knowl-edge of the thermal gradient on the other side of the inter-face (in the mush). Figure 2 shows schematically the heatbalance at the interface between the two magmasdescribed by equation (6). Equation (6) solves for the conju-gate heat transfer between the intrusion and the mush,which is limited by the medium with the slower heat trans-fer, in our case the mush because the intrusion is able toconvect (Carrigan, 1988).

It is, however, important to note that equations (1) and(6) relate the phase diagrams of the two magmas throughthe variation of crystallinity inside the andesitic intrusionand at the interface with the mush. For the andesiticmagma, we use MELTS with the major element composi-tion listed by Parat et al. (2008) for the Huerto andesite(San Juan Volcanic Field, Colorado) for a range of initialwater contents (from 1·5 to 6wt % H2O) and for pressuresof 1, 2 and 4 kbar). We also use MELTS to parameterizethe exsolution of volatiles (water only in this case; seebelow) as a function of temperature (see Fig. 3 for anexample of crystallinity^temperature and exsolution para-meterization for an underplating intrusion at 2 kbar con-taining initially 3·5wt % H2O).

Fig. 1. Schematic representation of the coupled mush^intrusion system.The two magmas exchange heat and the mush is subjected to injectionsof volatiles exsolved from the underlying intrusion.

Intrusion

Mush

sensible+latent heat

heat flux out

Fig. 2. Schematic description of heat transfer at the interface betweenthe intrusion and the mush. The heat flux out of the mush is balancedby changes in sensible heat (temperature) and melt fraction in themush at the interface.


850




The absence of CO2 in the MELTS calculation influ-ences both the saturation temperature and the stabilityfield of the various crystalline phases, and is expected tolead to more crystallization of anhydrous phases at highertemperature as CO2 decreases water activity. Because weare focusing on comparing the dynamics of the coupledsystem for different mush^intrusion conditions, we neglectthese effects in the following calculations. We nonetheless

obtain very reasonable saturation temperatures; for thecalculation at 4 kbar and 4·5wt % H2O, the melt reachesH2O saturation at about 8308C, which is consistent withthe experiments of Parat et al. (2008).The density of the exsolved water is calculated with the

Modified Redlich^Kwong (MRK) equation of state ofHalbach & Chatterjee (1982). We use a fit to the resultsobtained with the MRK equation to avoid inverting the

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

750 800 850 900 950

crys

talli

nity

temperature oC

intrusion: 2kbars-3.5 wt % H2O-0.0014 T + 1.55

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

750 800 850 900 950

volu

me

frac

tion

of e

xsol

ved

H2O

temperature oC

intrusion: 2kbars-3.5 wt % H2O-0.00035 T + 0.46

(a)

(b)

Fig. 3. (a) Calculation of the crystallinity^temperature relationship for an andesite [major element composition of the Huerto andesite fromParat et al. (2008)] with 3·5 wt % H2O at 2 kbar. (b) Calculation of the volume fraction of exsolved water for the same magma compositionand same pressure conditions. Both calculations were run with MELTS (Ghiorso & Sack, 1995).We use linear fits over a range of temperaturefrom 750 to 8508C to parameterize the crystallization and exsolution of water in the intrusion.


851




equation of state for the density at each node and for eachiteration (see Fig. 4).We obtain

rH2O&T ,P' # $112 ( 528T$0(381 % 127 ( 811P$1(135

% 112 ( 04T$0(411P0(033 &7'

for 600"T" 9008C and 300"P" 4000 bar. The densityof the volatile phase (water) in the intrusion varies by afactor of eight between the calculations at 1 and 4 kbar(below and above the supercritical point for water).We assume that the transport of exsolved volatiles after

the saturation point can be described by a multiphaseDarcy equation:

qH2O # kkr!rgmg

&8'

where k and kr are the permeability of the magma and therelative permeability for the volatile phase, respectively,and !r is the density contrast between the melt and thevolatile phase. Gas transport in a crystal slurry, as opposedto a rigid mush, is not expected to exhibit a Darcian behav-ior. Instead, at low Reynolds number (ratio of inertia toviscous forces), equation (8) has the general form of theStokes’ ascent velocity for a dilute suspension of bubbles,

where k and kr would then represent an average bubbleradius. Moreover, we expect that the presence of at least25^30 vol. % of crystals and the large viscosity contrastbetween the bubbles and the melt (*10^8) justifies this sim-plification. The closure of equation (8) requires expressionsfor both the permeability and the relative permeability.The permeability is related to the crystallinity by theCarman^Kozeny relation (Bear, 1972):

k # A&1$ wi'3

+1$ &1$ wi',2&9'

where the constant A is set to 2)10^12 m2, leading to a per-meability k#10^12 m2 at wi# 0·5.This choice of permeabil-ity^porosity relationship is consistent with the range ofporosities observed in our calculations (0·45^0·75). Manyempirical and theoretical expressions have been derivedfor the dependence of the relative permeability on the vola-tile volume fraction; these commonly reduce to powerlaws with exponent n* 4 (e.g. Brooks & Corey, 1964). Weuse the following expression:

kr&Sg' # S4g &10'

where Sg is the volume fraction of exsolved volatiles.Equation (10) neglects the effects of irreducible and

600 650

700 750

800 850

900 500 1000 1500 2000 2500 3000 3500 4000

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

H20

den

sity

in k

g/dm

3

Temperature °C Pressure in bars

fitModified Redlich-Kwong, Halbach and Chatterjee, 82

Fig. 4. Parameterization of the equation of state for water.We use the modified Redlich^Kwong model of Halbach & Chatterjee (1982).


852




residual saturation. As a correction to the non-purelyDarcian behavior of the gas in the crystal-slurry,we allowed gas transport below the residual satura-tion limit. This simplification is not valid for the mush,where the viscosity of the magma is much larger as aconsequence of its dacitic composition and highcrystallinity.

Crystal mushThe mush above the intrusion initially has a crystallinityof 55% and experiences both reheating and injection ofvolatiles from the intrusion. We solve for volatile massconservation:

@+rg&1$ wmush'Sg,@t

# $@&rgud,z'

@z&11'

where rg#rH2O, wmush is the crystallinity of the mush, Sgis the pore volume fraction occupied by the volatiles andud,z is the z-component of the Darcy velocity for the vola-tile phase and z is parallel to gravity. The boundary condi-tion at the interface between the mush and the intrusionrequires matching the volatile flux with equation (8). Weassume here that the melt is volatile-saturated and that nofurther degassing or dissolution of volatiles occurs withinthe mush. The flux of volatiles is obtained from

ud,z # $ kmushkr mush

mH2O

@

@zrH2O z& ' $ rmelt' (

gz) *

&12'

where g is the acceleration due to gravity and is countedpositive upwards, k and kmush and kr mush are respectivelythe permeability and relative permeability of the mush forthe volatile phase and mH2O is the dynamic viscosity ofthe volatile phase, which, for simplicity, was fixed at10^5 Pa s (Assael et al., 2000).The permeability of the mush evolves with time because

of the changes in porosity associated with partial meltingof the mush. We use the same permeability^porosity rela-tionship as equation (9).The relative permeability accountsfor the residual saturation; that is, the volume fraction ofthe pore space under which the mobility of the non-wettingphase is drastically reduced because of capillary effects:

kr mush #S4g $ S4residual1$ S4residual

: &13'

The residual saturation can be understood as athreshold value below which the mobility of thenon-wetting phase is negligible (see Fig. 5). It thereforeplays a central role in volatile transport in the mush.Owing to the lack of experimental constraints on theresidual saturation for exsolved water hosted in afeldspar-dominated mush saturated with a silicate melt,we use a value of Sresidual# 0·2, consistent with many natu-ral systems (Bear, 1972).

The crystallinity of the mush is related to temperatureusing a parameterization with a single free parameter b:

wmush # 1$ T $Tsol

Tliq $Tsol

" #b

, with 0 < b < 1: &14'

Tsol and Tliq are the solidus and liquidus temperatures,respectively set to 700 and 9508C, and b is a free parameterused to set different crystallization behaviors for themagma. For example, as b decreases to zero, the magmatends to crystallize mostly over a narrow range of tempera-ture just above the solidus (see Fig. 6).To follow the evolution of the crystallinity of the mush,

we solve the energy balance that includes heat diffusion,absorption of latent heat during the partial melting of themush and advection of heat by the volatile phase:

@&rmixcmixT'@t

# @

@z&cgrH2Oud,zT' % @

@zkmix

@T@z

" #

% rsL@wmush

@t:

&15'

In equation (15), the specific heat of the volatiles cg isassumed constant (3880 J/kgK; Lemmon et al., 2003),rH2O is calculated with the MRK equation of state [equa-tion (7)], and rs is the average density of the crystallinephase subjected to melting. Equation (15) assumes that thevolatile phase is locally in thermal equilibrium with themelt and crystals, which assumes a low Peclet number(i.e. Pe# ud,z R/k51, R being the average pore radius andk the average thermal diffusivity). The maximum Pecletnumber achieved in the simulations is about 10$2 for apore size of about 1mm.The thermal equilibrium assump-tion is, thus, a good approximation. The density, specificheat and thermal conductivity of the solid^melt^volatilesmixture are calculated with

rmix # rm&1$ wmush'&1$ Sg' % rswmush

% rH2O&1$ wmush'Sg&16'

cmix #rm&1$wmush'&1$Sg'cm%rswmushcs%rH2O&1$wmush'Sgcg

rm&1$wmush'&1$Sg'%rswmush%rH2O&1$wmush'Sg&17'

kmix #rm&1$wmush'&1$Sg'km%rswmushks%rH2O&1$wmush'Sgkg

rm&1$wmush'&1$Sg'%rswmush%rH2O&1$wmush'Sg&18'

where the subscripts s, m, g refer to solid, melt and vola-tiles, respectively. Table 1 lists the parameters used in thephysical model.

Numerical modelWe solve for the one-dimensional gas transport andenthalpy balance between the two magmas using an


853




iterative explicit finite-difference method. We use a nestediterative scheme that can be divided in two groups, (1)the enthalpy balance group and (2) the volatile transportgroup. We use an iterative solver to calculate the heattransport and thermal coupling between the two magmas,the crystallinity profile in the mush, the average crystalli-nity of the intrusion and the permeability profile in themush (enthalpy group). Once the variables converge towithin a tolerance (relative difference between two consec-utive iteration steps is lower than 10$12 typically), we fixthem and solve iteratively for the volatile transport,relative permeability of the mush, and thermal andmechanical properties of the volatile^melt^solid mix-ture, until convergence is reached. We then repeat theiterative process for the two parts of the scheme consecu-tively before proceeding to the next time step. Table 2 liststhe major input variables and the output that is calculated.We use similar thermal and mechanical properties,

as well as similar initial conditions for each calculation.We conducted four calculations with different power-lawexponents for the crystallinity^temperature relationship

[equation (14), b# 0·4, 0·5, 0·7 and 1 for each intrusion ini-tial water content (1·5, 2·5, 3·5, 4·5 and 6wt % H2O)and each pressure of emplacement (1, 2 and 4 kbar)].All the calculations have a 2 km thick mush discretized

with a resolution of 20m. We set the initial crystallinityof the mush to 0·55. Because we compare calculationswith the same initial crystallinity in the mush but withdifferent temperature^crystallinity relationships, the ini-tial temperature of the mush is not the same from one runto another. The initial temperature of the 500m thickintrusion is set to 8508C, about 208C above the water satu-ration conditions of the Huerto andesite composition at4 kbar (Parat et al., 2008). The calculations are run for1000 years with a time step of a few hundred seconds toensure stability. The mush is assumed to contain noexsolved volatiles initially. Each run is duplicated with anidentical test run except that in the test run the volatilesexsolved from the intrusion are not allowed to penetrateinto the mush. These control runs allow us to isolate andquantify the impact of volatiles on the overall thermalevolution of the system.

buoyant bubbles

Sg < residual saturation Sg > residual saturation

(a)

(d) (e)

(b) (c)

solid

wetting fluid

non-wettingfluid

Fig. 5. Schematic representation of capillary effects responsible for the residual saturation of a non-wetting phase. (a)^(c) show three snapshotsof the motion of a bubble (non-wetting phase) through a constriction calculated with the lattice Boltzmann method. The buoyancy forceworks against bubble deformation and the displacement of the wetting phase next to the solid. (d) A train of buoyant bubbles ascending througha saturated porous medium. At low saturation, the non-wetting phase is dispersed as bubbles, each of which is working against the forcesdescribed in (a)^(c). (e) At higher saturation (above the residual saturation) the mobility of the non-wetting phase is increased by severalorders of magnitude because the connected phase mobility now is controlled by the viscosity of the nonwetting phase (about 8^10 orders ofmagnitude smaller for silicic magmas and exsolved water).


854




RESULTSFor each run, we keep track of the temporal evolution ofthe intrusion in terms of average temperature, crystallinityand volume fraction of exsolved volatiles. Figure 7 shows

the temporal evolution of the average temperature ofthe intrusion and the temperature just above the interfacebetween the two magmas (in the mush) for an intrusionemplaced at 1 kbar, containing 4·5wt % H2O and a mushwith b# 0·4. The initial temperature difference is about1168C and is quickly reduced to about 108C over c. 10years because of the high heat flux from the intrusion tothe mush. After about 10 years, the temperature in theintrusion and in the lowest part of the mush both decrease,because of the cooling of the intrusion. The temperaturedifference at the interface between the two magmasis reduced to about 18C after about 1000 years. Figure 8shows the evolution of the average crystallinity andexsolved volatile fraction in the intrusion for the same cal-culation (1 kbar, 4·5wt % H2O). At 1 kbar, the intrusioncontains about 23 vol. % volatiles at the emplacementtemperature (8508C). The volatile volume fraction isquickly reduced because of the rapid transfer to the mush[volatile mobility depends strongly on the volatile volumefraction from equations (8) and (10)].We also monitor the evolution of porosity, temperature

and pore volume fraction occupied by the volatiles withdepth in the mush. Figure 9 shows results after 1000 yearsfor a mush with a temperature^crystallinity relationshipwith b# 0·4 and for an intrusion emplaced at 1 kbar with4·5wt % H2O. Figure 9a shows the porosity (or extentof melting) and Fig. 9b the temperature in the mush. Thevertical distance is normalized by the thickness of the

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

crys

talli

nity

(T - Tsol)/(Tliq - Tsol)

Pagosa Peak Dacite - MELTS b = 0.4 best fit to dacite comp.

b = 0.1b = 0.5

b = 1

Fig. 6. Crystallinity^temperature relationships for the mush from equation (14) for different values of b. As b decreases towards zero, the systemtends to crystallize more just above the solidus temperature. The crystallinity^temperature relation for the Fish Canyon magma body (dacite)calculated with MELTS is shown as a reference. The Fish Canyon magma is consistent with an exponent b50·4.

Table 2: List of input and output variables in the model

Symbol Description Input Output

b T$ |mush power-law

exponent

0·4, 0·5, 0·7, 1

wt % H2O initial H2O in intrusion 1·5, 2·5, 3·5, 4·5, 6

Vr volume ratio (intrusion/

mush)

1:4!

Tintr (0) initial T of intrusion 8508C!

wmush (0) initial crystallinity of

mush

0·55!

T(z) T profile in mush solved for

wmush(t) crystallinity profile in

mush

solved for

Tintr(t) average T in intrusion solved for

wintr(t) average intrusion

crystallinity

solved for

!Variables that are fixed to the same value for all the runs.


855




mush (2 km). The volume fraction of volatiles in the porespace (Fig. 9d) exhibits a more interesting behavior. First,volatiles rise through more than half of the mush (morethan 1km) and much further than the melting front (seeFig. 9a). Second, the maximum saturation of 0·2 is consis-tent with our choice of residual saturation, as the volatilesbecome much more mobile above this threshold. The pro-file, however, shows a decrease in pore saturation betweendistances of 0·1 and 0·4. Figure 9c shows the profile of theproduct of the porosity and the pore volume fraction ofvolatiles, and shows that the volume of volatiles monotoni-cally decreases until reaching a plateau consistent with20% of the pore space at 45% porosity all the way to thevolatile propagation front. This illustrates that the reduc-tion of Sg between distances 0·1 and 0·4 from the intrusionis the consequence of melting and increase of pore spaceat constant volatile volume (Fig. 10). The mobility of thevolatile phase is controlled by the local volume of volatilesin the pore space [equation (10)].At 1 kbar, the low density of the volatile phase

(0·1^0·2 kg/m3) allows it to reach residual saturation effi-ciently and propagate through the mush ahead of the melt-ing front. As the melting front progresses behind thevolatile front, the pore space increases and more volatilesare required to keep the melting region at residual satura-tion. If the increase in pore volume by melting is locallyfaster than the flux of volatiles, Sg decreases below theresidual saturation value (see Fig. 10), leading to the forma-tion of two large-scale slug regions of volatiles separatedby a low hydraulic conductivity region (below residual sat-uration). The volatile slug that detaches ahead of the

melting front (distance from the intrusion greater than0·2 in Fig. 9b) carries little excess enthalpy beyond themain melting front. As the crystallinity^temperaturepower-law exponent b increases the segmentation of thevolatile-rich part of the mush is reduced (Fig. 11), as theincrease in pore volume owing to melting is more equallydistributed over a wide range of temperature.Figure 12 shows the profiles for porosity, temperature, Sg

and fSg for a similar calculation in which the intrusion isemplaced at 4 kbar. In this case, the melting front propa-gates ahead of the volatile front and the features observedin Fig. 9 are not present. The melting front has not propa-gated as much as for the 1 kbar caseçthis is mostly theconsequence of low volatile mobility. The thermal conduc-tivity of water-rich volatiles (kH2O# 0·3; Lemmon et al.,2003) is about an order of magnitude lower than for themelt or crystals. Volatiles thermally insulate the mushfrom the intrusion because of their low thermal conductiv-ity (Bagdassarov & Dingwell, 1994). When the volatilesare mobile (when they reach the residual saturation), theheat they advect upwards can compensate for the negativeimpact they have on diffusive heat transfer.We will explorethis effect in more detail later.The rate of cooling and crystallization of the intrusion

depends on three main parameters: (1) the pressure atwhich the intrusion is emplaced, as this affects the phasestability of the different crystallizing phases; (2) the watercontent of the intrusion, for the same reasons; (3) thepower-law exponent b of the overlying mush. The last isimportant as it controls the initial temperature of themush (we fix the initial crystallinity) and also controls

805

810

815

820

825

830

835

840

845

850

0.1 1 10 100 1000

tem

pera

ture

o C

time (years)

intrusionmush lower boundary

Fig. 7. Average temperature of the intrusion and the intrusion^mush boundary with time.The andesitic intrusion is emplaced at a pressure of 1kbar and contains 4·5wt % water. The mush crystallinity^temperature is set with a power-law exponent b# 0·4.


856




the partitioning of heat delivered by the intrusion into sen-sible and latent heat.Figure 13 compares the average temperature and crystal-

linity of the intrusion (at 1 or 2 kbar) and the porosity ofthe mush just above the contact with the intrusion after1000 years. Each contour plot is shown as a function ofthe power-law exponent b for the mush and the initialwater content of the intrusion. The cooling rate of theintrusion decreases with increasing b because of the lowerinitial temperature difference between the two magmas athigh b. The slower cooling at high b is also a consequenceof the lower latent heat buffering of the mush; that is, the

heat from the intrusion is partitioned primarily into sensi-ble heat in the mush, which reduces more efficiently thetemperature difference between the magmas.The dependence of the final temperature of the intrusion

on its water content is more complicated. At 1 kbar, thefinal average temperature of the intrusion increases withwater content. As volatiles exsolve and migrate towardthe overlying mush they carry heat and reduce the temper-ature difference between the intrusion and the lowest partof the mush, and thus reduce the subsequent heat flow outof the intrusion. At 2 kbar, the situation is slightly different,with a peak of high average final temperature for the

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 100 200 300 400 500 600 700 800 900 1000

volu

me

frac

tion

Ave

rage

cry

stal

linity

time (years)

exsolved volatiles

0.33

0.335

0.34

0.345

0.35

0.355

0.36

crystallinity

Fig. 8. Evolution of the average crystallinity and volume fraction of exsolved volatiles in the intrusion. The characteristics of the mush and theintrusion are similar to those in Fig. 7.


857




intrusion at about 2·5wt % H2O. For dry intrusions(below 2wt % H2O), the cooling and crystallization ofthe intrusion does not lead to exsolution of water. Forintrusions containing between 2 and 3·5wt % H2O, themass of volatiles injected into the mush is relatively small.Moreover, at 2 kbar the average density of the volatilephase is almost twice the density at 1 kbar. As a conse-quence, the small mass of volatiles injected into the mushdoes not reach residual saturation and the volatilesremain immobile just above the interface between the twomagmas. As volatiles have a much lower thermal conduc-tivity than both melt and crystals they thermally insulatethe intrusion and prevent efficient cooling. This ‘thermosbottle effect’ (Carrigan, 1988) caused by a gas-rich layerbetween two magmas has been previously described byBagdassarov & Dingwell (1994). At higher initial watercontents in the intrusion, the greater exsolution and injec-tion rate of volatiles into the mush allows residual satura-tion to be reached and the volatiles become mobile in the

mush, advecting heat away from the interface between themagmas. The porosity of the mush at the contact with theintrusion is consistent with these observations.We define three lengthscales to characterize the melting

efficiency and volatile transport in the mush for each calcu-lation. The first lengthscale dm0 represents the meltingfront position in the mush measured from the contact withthe intrusion in the absence of volatiles. It is obtainedfrom the control runswhere the volatile phase is not injectedinto the mush.The second lengthscale dm1 is similar, but forruns where volatiles were allowed to penetrate into themush. The last lengthscale dg characterizes the distancetraveled by volatiles in the mush from the contact with theintrusion.Wedefine two dimensionless ratiosR1andR2:

R1 #dgdm1

&19'

represents the efficiency of volatiles to be transported intothe mush, where R141 indicates calculations where the

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

vertical distance from intrusion

porosity

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1


volatiles volume

(a) (b)

(c) (d)

Vol

ume

frac

tion

(por

osity

)V

olum

e fr

actio

n

0

0.05

0.1

0.15

0.2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1


volatile pore saturation

Por

e vo

lum

e fr

actio

n

730

740

750

760

770

780

790

800

810

820

830

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1


temperature

Tem

pera

ture

Fig. 9. Results obtained after 1000 years; the characteristics of the mush and the intrusion are similar to those in Fig.7. (a) Profile of porosity fwith depth in the mush (zero is the mush^intrusion boundary and one is the top of the 2 km thick mush). (b) Temperature profile. (c) Localvolume fraction of volatiles (#fSg). (d) Volume fraction of the pore space occupied by volatiles, Sg.


858




volatiles are transported ahead of the melting front (e.g.Fig. 9). The second dimensionless ratio is given by

R2 #dm1

dm0: &20'

This is the ratio of the melting front distance when volatilesare accounted for to when they are not. R2 therefore iso-lates the effect of volatiles on the melting of the mush.Figure 14 shows contour plots of R1 and R2 for three

intrusion emplacement pressures as function of b and theinitial water content of the intrusion. The results for R1 aresimilar for 1 and 2 kbar.Volatile transport is more efficientfor larger values of b and higher intrusion water contents.The dependence of R1 on b is consistent with the observa-tion of the effect of b on the volatile volume fractionshown in Fig. 11. At larger values of b the decrease in

volume fraction induced by the increase of pore space isreduced.At 2 kbar, we observe similar results, but shifted to

higher intrusion water contents and lower R1 as expectedbecause of the higher density of the volatiles at higher pres-sures. The results at 4 kbar are different. Only the mostfavorable cases, low b (faster cooling and exsolution ratefrom intrusion) and high water content in the intrusionallow the volatiles to propagate ahead of the melting front(R141).The contour plots of R2 (Fig. 14) characterize the impact

of volatiles on the partial melting of the mush. R241 repre-sents calculations where volatiles enhance the melting ofthe mush, whereas R251 indicates that volatiles suppressmelting. At 1 kbar, no calculations lead to R251. At lowwater contents (53wt %), no volatiles are injected into

View along gravity axis (from above)

Solid

Gas

melt

Solid

Gas

melt

Solid

Gas

melt

Solid

Gas

melt

t1

t1

t2

t2

(a)

(b)

melting more efficient than injection of volatiles Sg(t1) > Sg(t2)

melting less efficient than injection of volatiles Sg(t1) < Sg(t2)

Fig. 10. Schematic description of the dilution effect experienced by the volatile fraction during the increase of pore space associated with melt-ing. Case (a) shows an example where the melting rate is faster than the injection rate, leading to a dilution effect of the volatile phase in thepore space (Sg decreases with time). Case (b) shows the opposite situation, where the volatile injection rate is high enough to compensate forthe increase in pore space associated with melting. In this case, the local pore fraction occupied by the volatile phase increases with time andcan potentially reach the residual saturation threshold over which it becomes mobile and buoyantly rises in the mush.


859




the mush and R2#1. At higher pressure (2 and 4 kbar), thesame result is obtained but shifted to higher water contentsas expected. Nevertheless, a major difference appears. Aregion where R251 (i.e. where volatiles decrease the melt-ing efficiency) is observed at lower water contents and lowb.

DISCUSS IONEffect of meltingPartial melting increases the hydraulic conductivity of themush as the permeability increases with increasing poros-ity (melt fraction). For multiphase flows in porous media,the effect of melting on the transport of each phasedepends on their wetting characteristics. For a fixedvolume of non-wetting phase, its saturation scales with

Sg /1

1$ w&21'

where 1 ^ w is the local porosity of the mush. As a conse-quence, the dependence of the hydraulic conductivity ofthe non-wetting phase on the porosity becomes

K / kkr /1

1$ w: &22'

The partial melting of the mush therefore has a negativeimpact on volatile transport. This effect becomes evenmore important when the local volatile volume fraction isjust above the residual saturation as observed in Fig. 9. Asa consequence, for each calculation, as the lowermost part

of the mush is melting and reaching higher porosities,more volatiles have to be injected to reach the residual sat-uration and become mobile. This effect is clearly observedin our results, as calculations with larger b (which reducesthe amount of partial melting at high crystallinity) allowvolatiles to propagate further.The mobility of the volatiles thus depends on two com-

peting effects: melting and injection rate from the intru-sion. To better understand these effects we discuss aconceptual model with a single pore (see Fig. 10). Thevolume fraction occupied by volatiles in the pore increasesbecause of volatile injection and decreases because of theincrease in pore space by melting. Using mass balance forthe volatiles, we obtain

V0pdSgdt

# qvol $ SgV0pdfdt

&23'

where V0p is the initial pore volume, and qvol is the volumet-

ric injection rate of volatiles. The relative importance ofthe source and sink terms for Sg can be cast in terms of adimensionless number z:

z - !m!v

# qvolVp

dfdt

&24'

where !m and !v are respectively the timescales for meltingand volatile injection. For z41, volatiles can accumulatein the pore space, reach the residual saturation andbecome mobile in the mush. On the other hand, whenz51, melting dominates and keeps the volume fraction ofthe volatiles below the residual saturation. Mobility of the

0

0.05

0.1

0.15

0.2

0.25

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1vertical distance from intrusion

b=0.4b=0.5b=0.7

b=1

Sg

Fig. 11. Comparison between runs with different crystallinity^temperature power-law exponent b. The intrusion is emplaced at 1 kbar with4·5wt % H2O.


860




volatile phase (i.e. z41) requires either a small meltingrate or fast injection rate of volatiles into the mush, or acombination of both. Smaller melting rates occur forlarger b values. However, the slower cooling rate at high bdecreases the volatile injection rate as observed in Figs 13and 14. For R141, the negative effect of melting on themobility of volatiles has to be compensated by the highinjection rate (i.e. z41). At 4 kbar, the transport of vola-tiles is limited by the volume of volatiles injected into themush and requires the more water-rich conditions and thelargest initial temperature difference between the twomagmas.

Effect of volatilesAnother important result from the calculations is the effectof volatiles on the thermal evolution of the two magmas.When the degassing of the intrusion is such that volatilescan travel upwards through the mush (z41), the volatilesadvect heat and push the melting front forward. Theexcess enthalpy advected by the volatiles is limited, as

substantial melting of the mush would locally drive the vol-atile phase under the residual saturation limit (z51). Forcases where the volume of volatiles injected into the mushis too low to reach residual saturation in the lowermostpart of the mush, volatiles affect only the overall heattransfer because of their low thermal conductivity. Theythermally insulate the mush from the intrusion and, as aresult, slow down the diffusive heat transfer, i.e. R251(see Fig. 15). In our calculations, the thermal conductivityof the volatiles, the melt and solids are set respectively to0·3, 1·4 and 2W/mK. As a consequence, thermal insula-tion associated with the presence of volatiles includes twocontributions: a direct contribution from the low thermalconductivity of the volatile phase and an indirect contribu-tion if volatiles increase the degree of partial melting ofthe mush locally, replacing solids with melt with a lowerconductivity (1·4 instead of 2W/mK; Murase &McBirney, 1973; Bagdassarov & Dingwell, 1994).The magnitude of the thermal insulation associated with

a volatile-rich immobile layer depends on the choice for

0.45

0.5

0.55

0.6

0.65

0.7

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1


porosity

Vol

ume

frac

tion

(por

osity

)

0

0.05

0.1

0.15

0.2

0.25

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

volatile pore saturation


Por

e vo

lum

e fr

actio

n

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

volatiles volume


Vol

ume

frac

tion

730

740

750

760

770

780

790

800

810

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

temperature


Tem

pera

ture

(a) (b)

(c) (d)

Fig. 12. Results obtained after 1000 years.The characteristics of the mush and the intrusion are similar to those of Fig.7, except that the pressure(depth) is 4 kbar at the mush^intrusion boundary. (a) Profile of porosity f with depth in the mush (zero is the mush^intrusion boundary andone is the top of the 2 km thick mush). (b) Temperature profile. (c) Local volume fraction of volatiles (#fSg). (d) Volume fraction of the porespace occupied by volatiles, Sg.


861




0.4

0.5

0.6

0.7

0.8

0.9

1

816

820

824

828

832

836

0.4

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0.7

0.8

0.9

1

0.34

0.36

0.38

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0.42

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0.46

2 3 40.4

0.5

0.6

0.7

0.8

0.9

1

0.55

0.6

0.65

0.7

Average temperature of intrusion

Average crystallinity of intrusion

Porosity of mush in contact with intrusion

b

b

b

wt % H2O wt % H2O

1 kbar

1 kbar

1 kbar

0.4

0.5

0.6

0.7

0.8

0.9

1

816

820

824

828

832

836

2 3 4 5 60.4

0.5

0.6

0.7

0.8

0.9

1

0.26

0.3

0.34

0.38

0.42

0.46

2 3 4 5 60.4

0.5

0.6

0.7

0.8

0.9

1

0.55

0.6

0.65

0.7

2 kbar

2 kbar

2 kbar

Fig. 13. The two columns compare the results for the average temperature and crystallinity of the intrusion after 1000 years for calculations inwhich the pressure at the intrusion is set to 1 and 2 kbar. The x-axis and y-axis of these contour plots are respectively the initial water contentof the intrusion and the power law exponent b, defining the temperature^crystallinity relationship in the mush. The porosity of the mush justabove the intrusion is also shown for the calculations at 1 and 2 kbar.


862




2 3 40.4

0.5

0.6

0.7

0.8

0.9

1

0.5

1

1.5

2

2.5

3

3.5

4

2 3 40.4

0.5

0.6

0.7

0.8

0.9

1

1

1.02

1.04

1.06

1.08

1.1

1.12

1.14

1.16

2 3 4 5 60.4

0.5

0.6

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0.9

1

0

0.5

1

1.5

2 3 4 5 60.4

0.5

0.6

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0.85

0.9

0.95

1

1.05

1.1

2 3 4 5 60.4

0.5

0.6

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0.9

1

0.1

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0.5

0.6

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0.8

0.9

1

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

b

wt % H2O

1 kbar 1 kbar

b

b

wt % H2O

2 kbar 2 kbar

4 kbar 4 kbar

R1=dg/dm1 R2=dm1/dm0

Fig. 14. The left column shows the efficiency of the volatiles to rise ahead of the melting front in the mush for different pressures. The rightcolumn compares the melting front position with and without volatiles for three pressures. (For further details, see the main text.)


863




the averaging of the mixture properties [equation (16)].Weuse mass averages because the product of the specific heatand the local temperature has to be integrated over themass of the body to provide the sensible enthalpy fraction.This choice of averaging, however, provides a crudeapproximation for the thermal conductivity of a mixture.A more accurate estimation of the mixture thermal con-ductivity would be obtained using the bounds derived byHashin & Shtrikman (1963). According to this model, thelower and upper bound for the thermal conductivity areboth overestimated by respectively up to 10^20% with ourmass averaging and therefore predict a stronger thermalinsulation by volatiles. The calculation of these upper andlower bounds is straightforward but generates discontinu-ities in the mixture thermal conductivity owing to its stron-ger dependence on the volatile volume fraction. Thediscontinuity arises from the step function distribution ofvolatiles controlled by the residual saturation. For the sakeof numerical simplicity, we thus use mass averages for the

thermal conductivity. The extent of melting generated bythe advection of volatiles will remain mostly unaffectedby this choice, as the thermal conductivity of the mixtureaffects only the heat diffusion term.We emphasize that theoverall trend of the results will remain similar, but themagnitude of R1 and R2 would be different.

Effect of convectionIn all calculations, we did not account for the possibleonset of convection within the mush once the crystallinitydecreases below the rheological lock-up (w50·50) in alayer thick enough to become unstable. The presence ofvolatiles injected from the intrusion can also lower theaverage density at the base of the defrosted mush and con-tribute to gravitational instabilities. Convection willincrease the overall heat transfer from the intrusion to themush and accelerate the cooling of the intrusion. As aresult, the injection rate of volatiles to the mush is expectedto increase, but the delivery rate of volatiles to the melting

Melting front

Volatile penetration front

Silicic mush

Mafic underplating

Dry magmaticenvironment

Wet magmaticenvironment

Fig. 15. Melting scenarios in dry and wet magmatic provinces. In the dry case, volatiles stall at the interface between the intrusion and theoverlying mush and thermally insulate both magmas. In the wet case, the mobility of volatiles enhances the upward propagation of the meltingfront and allows the defrosting of the mush.


864




front in the mush can be substantially slowed down asexsolved bubbles have to separate efficiently from the con-vecting magma. The separation of the bubbles from theconvecting magma depends on the viscosity of themagma and the average bubble size (Cardoso & Woods,1999; Namiki et al., 2003). Convective currents will be lim-ited for the parameter range we considered, as efficientmelting scenarios require small b values and layers of highmelt fraction (above 60^65%) barely extend over a fewtens of meters. Moreover, with time, the lowermost part ofthe mush cools with the intrusion after the efficient initialreheating, leading to decreasing melt fraction in thelowest part of the mush after a few tens of years.

Questions revisitedIn the Introduction we listed several questions relative tothe thermal evolution of the two magma bodies. In thelight of the results of this study, we revisit these questions.

What features control the mobility of volatiles through amush?There are three major controls on the mobility of volatilesthrough a mush. If the advection of volatiles is associatedwith the advection of enthalpy, then their mobility is

controlled by (1) the flux of volatiles, (2) the ambient pres-sure and (3) the crystallinity^temperature relationship inthe mush. As the mobility of volatiles in the mush is con-trolled by the volume fraction they occupy [see equation(13)], the flux of volatiles and the pressure constrain thevolumetric rate of accumulation of volatiles locally,whereas the crystallinity^temperature relationship of themush describes the increase in pore space resulting fromthe flux of enthalpy associated with the volatile flux. Tosummarize, the mobility of volatiles is controlled by thevolume fraction they occupy in the mush. Partial meltingof the mush decreases the mobility of volatiles (assumingvolatiles are the non-wetting phase in the melt^volatile^solid system), whereas lower pressure increases theirmobility.

Can the vertical transport of volatiles enhance or prevent thedefrosting (partial melting of the crystalline framework)of a mush?Our results show that once the volatiles are mobile, theexcess enthalpy they advect away from the mush^intrusioninterface enhances the defrosting of the mush. This, how-ever, requires relatively low pressures, high permeabilityand/or water-rich (saturated) intrusions. If the intrusion is

0

2

4

6

8

10

12

14

16

40 45 50 55 60 65 70 75 80

Basalt BasalticAndesite

AndesiteDacite

Trachybasalt

Trachyandesite

Trachydacite

Trachyte

Rhyolite

Dry, hotspot-related magmatic activityYellowstone - Snake River Plain (YSRP)Wet, calc-alkaline seriesGreat Basin units

Compositional gap YSRP

= dry, uneruptable mushes

SiO2 (wt%)

Na 2

O +

K2O

(w

t%)

Fig. 16. Total alkalis^silica diagram showing the wide compositional gap present in the dry, hotspot-related Yellowstone Snake River Plain(YSRP) units, whereas the wet, calc-alkaline series of the Oligocene Great Basin display a continuous range of compositions from basaltic ande-site to rhyolite. We argue that this compositional gap is a consequence of the ineruptability of mushes with intermediate compositions in theYSRP because of their lower volatile content, leading to (1) a delay in volatile exsolution and (2) inefficiency of gas-driven defrosting (gas spar-ging) of rheologically locked mushes (modified from Christiansen & McCurry, 2008).


865




unable to deliver enough volatiles to the mush, the low ther-mal conductivity of the volatiles thermally insulates the twomagmas and therefore preventsmelting in themush.

What explains the paucity of crystal-rich ignimbrites in ‘dry’(extensional or hotspot) tectonic environments?Large crystal-rich dacitic eruptions (‘MonotonousIntermediates’) are common in continental arc settings,with examples found in the high Andes (Lindsay et al.,2001), and in the Oligocene magmatic ‘flare-up’ in theWestern USA (Lipman, 2007; Christiansen & McCurry,2008). On the other hand, such crystal-rich intermediateignimbrites are yet to be found in hotspot or continentalrifts (e.g. Yellowstone^Snake River Plain area; seeFig. 16). This observation has led some researchers tospeculate that mushes do not exist in the source regionsof crystal-poor rhyolites in those tectonic settings(Christiansen, 2005; Streck & Grunder, 2008).On the basis of this study, we propose an alternative sce-

nario: dry mushes are nearly impossible to erupt. Toappear in the volcanic record, a locked crystal mushneeds to be defrosted. In hotspot or extensional magmaticenvironments, the low initial volatile content of the under-plating intrusions results in slow gas transfer with a nega-tive (insulating) impact on the remobilization of the mush(R251, see Fig. 14). In continental arc settings, however,an intrusion initially containing more than 4wt % of vola-tiles will generate a high enough injection rate of volatilesfor them to become mobile in the mush (z41), enhancingdefrosting (Fig. 17).

What is the effect of the mush composition on the thermalevolution of the two magma bodies?The mush composition controls its crystallinity^tempera-ture relationship. At a crystallinity of the mush above 0·5,the partitioning of enthalpy between sensible and latentheat during the heating of the mush by the intrusiondepends on its composition. For more evolved magmas,the changes of crystallinity resulting from small additionsof enthalpy can be significant (b" 0·5), whereas formagmas further away from the haplogranitic eutectic com-position the changes in crystallinity can be substantiallysmaller and enthalpy is mostly absorbed by sensible heat(temperature change). The latter case is characterized byz41 and volatiles can rise and move beyond the meltingfront provided that the intrusion contains enough volatiles.For mushes with a composition closer to the eutectic, theincrease in pore space associated with the heat diffusedfrom the intrusion can, in some cases, prevent the volatilesfrom ascending or, when enough volatiles are available,lead to the formation of separate gas slugs as indicated inFig. 11.

CONCLUSIONSIn this study, we calculate the enthalpy coupling between acooling and degassing intrusion and an overlying crystalmush.We quantify the partial melting of the mush for dif-ferent crystallinity^temperature relationships, at differentpressures and with different initial water contents for theintrusion. We show that partial melting of the mushreduces the mobility of the volatiles because the ability ofvolatiles to ascend through the mush depends on thevolume fraction they occupy in the pore space. This effectcouples the fate of volatiles exsolved from the underplatingintrusion to the composition of the mush.Our calculations demonstrate that volatiles can play two

opposite roles in the thermal evolution of the mushdepending on their mobility in the mush. At high volatilefluxes, the enthalpy they advect away from the interfacebetween the two magmas favors remobilization. In con-trast, low volatile fluxes partially prevent the reactivationof the mush by insulating it from the intrusion. Theseopposite effects at low and high volume fraction of volatilescan explain the paucity of erupted crystal-rich ignimbritesin dry tectonic environments where mushes of intermedi-ate composition cannot be rejuvenated and erupted oncethey reached their rheological lock-up point.

ACKNOWLEDGEMENTSWe thank our colleagues Joe Dufek and George Bergantzfor unfailing support and numerous fruitful discussions onthe topic of this paper. Insightful comments by an anon-ymous reviewer, F. Spera, J. Wolff, and editor WendyBohrson are gratefully acknowledged.

2 3 4 5 60.4

0.5

0.6

0.7

0.8

neutral(gas has no effect)

insu

latin

g

Volatile effect on heat transfer

defrosting

“dry” silicicmushes

“wet” silicicmushes

b

wt % volatilesFig. 17. The different regimes of mush defrosting induced by volatileexsolution from an underplating intrusion at 2 kbar. b is the exponentof the crystallinity^temperature relationship [equation (14)].


866




FUNDINGC.H. and M.M. were supported by NSF EAR 0608885and the Larsen Fund, and O.B. was supported by NSFEAR grant 0809828.

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